The new IAU recommended transformation between the Celestial and Terrestrial Reference Frame and its implementation in Matlab

between the Celestial and Terrestrial Reference Frame and its implementation in Matlab

Matthias Weigelt ^∗ Nico Sneeuw

∗University of Calgary, Department of Geomatics Engineering, [email protected]

Outline

• Theory of the transformation - celestial intermediate pole

- celestial/terrestrial ephemeris origin, earth rotation angle

• Implementation in Matlab

• Conclusions

Outline Theory Implementation Conclusions

Theory of the transformation

Motivation:

• VLBI outmatches the accuracy of the old precession- nutation model (1 mas).

⇒ Need for more precise definitions of time-space transformations

• IERS uses the new model since January 1st, 2003 Basic formula:

x_CRS = Q(t)R(t)W(t)x_TRS Q(t) precession-nutation R(t) earth rotation

W(t) polar motion

Outline Theory (1/3) Implementation Conclusions

Usage of the Celestial Intermediate Pole (

)

(source: IERS Technical Notes No.29)

• its motion in the CRS is specified by the motion of the Tisserand mean axis of the Earth with periods greater than two days,

• precession-nutation model:

- ^IAU2000^A: 0.2 mas - ^IAU2000^B: 1 mas

• its motion in the ^TRS is provided by observations and by a model including high frequency variations,

• separates the celestial (precession- nutation) from the terrestrial (polar motion) components.

Outline Theory (2/3) Implementation Conclusions

Usage of the Celestial/Terrestrial Ephemeris Origin (

/

) and the Earth Rotation Angle (

)

• separates precession-nutation from the Earth rotation

• independent from the theory of Earth’s orbital motion around the Sun and the precession-nutation model

(source: IERS Technical Notes No.29)

• ERA is the angle between the TEO and the CEO along the equator reckoned from the TEO

• ERA is linearly related to UT1 and is used instead of the Greenwich Sidereal Time

Outline Theory (3/3) Implementation Conclusions

Implementation

Why using Matlab?

• ubiquity in the scientific research area

• ease of use

Possible ways of implementation:

1. Use the classical procedures and apply corrections for precession and nutation.

2. Use the new approach (^CIP,^CEO,^TEO,^ERA)

Outline Theory Implementation (1/4) Conclusions

Preparation

1. Import ^EOP-data from file finals2000A.data (provided by ^IERS)

2. Time:

• TT as input time

• derivation of MJD

• derivation of ^UT1 → ERA

• derivation of ^GMST → arguments

3. Arguments:

• luni-solar nutation

• planetary nutation

Outline Theory Implementation (2/4) Conclusions

Polar Motion and

• Motion of the ^CIP in the ^ITRS: x_p

y_p

=

x_IERS y_IERS

+

x_tidal y_tidal

+

x_nutation y_nutation

s⁰ = −47µas · t

• Transformation from the ^ITRS to the intermediate system:

W(t) = R₃(−s⁰) · R₂(x_p) · R₁(y_p)

• Transformation due to the Earth rotation using ^ERA θ:

R(t) = R₃(−θ)

Outline Theory Implementation (3/4) Conclusions

Motion of the

in the

• Series development for X,Y and s - ^IAU2000^A: 1365 values

- ^IAU2000^B: 81 values

• Transformation from the intermediate system to the ^CRS:

Q(t) =





1 − aX² −aXY X

−aXY 1 − aY ² Y

−X −Y 1 − a(X² + Y ²)



 · R₃(s)

where:

a = 1

1 + Z ≈ 1

2 + 1

8 X² + Y ²

• Possibility of including observed corrections as provided by the IERS

Outline Theory Implementation (4/4) Conclusions

Conclusions

• Need for more precise definitions of time-space transformations

• Usage of

,

,

,

• Two possible ways of calculation

• Step by step implementation in Matlab

• Accuracy:

-

2000

: 0.2 mas -

2000

: 1 mas

Outline Theory Implementation Conclusions

Questions ?

Outline Theory Implementation Conclusions